3rd Quintile, 1962 to 1996 g 0.83 1.56 1.00 1.28 0.57 1.03 1.96 1.50 1.55 1.14 p-value 0.502 0.016 0.266 0.074 0.903 0.243 0.001 0.023 0.016 0.150 gt~ ' ! 0.95 0.94 0.66 0.76 0.61 0.82 1.45 1.61 1.17 1.01 p-value 0.326 0.346 0.775 0.613 0.854 0.520 0.031 0.012 0.131 0.258 gt~ ; ! 1.05 1.43 0.93 1.14 0.63 0.80 0.93 0.78 0.59 0.86 p-value 0.223 0.033 0.350 0.147 0.826 0.544 0.354 0.578 0.878 0.450 g Diff. 1.02 1.14 0.45 0.48 0.50 0.89 0.66 0.91 0.72 1.15 p-value 0.246 0.148 0.986 0.974 0.964 0.413 0.774 0.383 0.670 0.143 4th Quintile, 1962 to 1996 g 0.72 0.61 1.29 0.84 0.61 0.84 1.37 1.37 0.72 0.53 p-value 0.683 0.852 0.071 0.479 0.855 0.480 0.048 0.047 0.682 0.943 gt~ ' ! 1.01 0.95 0.83 0.96 0.78 0.84 1.34 0.72 0.62 1.01 p-value 0.255 0.330 0.504 0.311 0.585 0.487 0.056 0.680 0.841 0.258 gt~ ; ! 0.93 0.66 1.29 0.96 1.16 0.69 0.64 1.16 0.69 0.85 p-value 0.349 0.772 0.072 0.316 0.137 0.731 0.810 0.136 0.720 0.468 g Diff. 1.10 0.97 0.64 1.16 1.31 0.78 0.64 0.92 0.66 1.10 p-value 0.175 0.301 0.804 0.138 0.065 0.571 0.806 0.363 0.780 0.176 Largest Quintile, 1962 to 1996 g 1.25 1.16 0.98 0.48 0.50 0.80 0.94 1.76 0.90 1.28 p-value 0.088 0.136 0.287 0.977 0.964 0.544 0.346 0.004 0.395 0.077 gt~ ' ! 1.12 0.90 0.57 0.78 0.64 1.17 0.91 0.87 0.64 1.20 p-value 0.164 0.386 0.906 0.580 0.806 0.127 0.379 0.442 0.802 0.114 gt~ ; ! 0.81 0.93 0.83 0.61 0.69 0.81 0.73 0.87 0.46 0.88 p-value 0.522 0.350 0.495 0.854 0.729 0.532 0.661 0.432 0.982 0.418 g Diff. 0.71 0.54 0.59 0.64 0.76 1.21 0.85 1.11 0.54 0.79 p-value 0.699 0.934 0.874 0.800 0.607 0.110 0.467 0.170 0.929 0.552 All Stocks, 1962 to 1966 g 1.29 1.67 1.07 0.72 0.75 1.32 1.20 1.53 2.04 1.73 p-value 0.072 0.007 0.202 0.671 0.634 0.062 0.112 0.018 0.001 0.005 gt~ ' ! 0.83 1.01 1.04 0.80 0.63 1.80 0.66 1.84 1.03 1.54 p-value 0.499 0.260 0.232 0.539 0.826 0.003 0.771 0.002 0.244 0.017 gt~ ; ! 1.13 1.13 0.84 0.84 0.58 1.40 1.12 0.83 1.09 1.16 p-value 0.156 0.153 0.480 0.475 0.894 0.040 0.163 0.492 0.183 0.135 g Diff. 0.65 0.71 0.75 0.76 0.60 1.90 0.68 1.35 0.73 0.83 p-value 0.799 0.691 0.629 0.615 0.863 0.001 0.741 0.052 0.657 0.503 continued Foundations of Technical Analysis 1755 Table VII—Continued Statistic HS IHS BTOP BBOT TTOP TBOT RTOP RBOT DTOP DBOT All Stocks, 1967 to 1971 g 1.10 0.96 0.60 0.65 0.98 0.76 1.29 1.65 0.87 1.22 p-value 0.177 0.317 0.867 0.797 0.292 0.606 0.071 0.009 0.436 0.101 gt~ ' ! 1.02 0.80 0.53 0.85 0.97 0.77 0.71 1.42 0.97 1.06 p-value 0.248 0.551 0.943 0.464 0.303 0.590 0.700 0.035 0.300 0.214 gt~ ; ! 1.08 0.86 0.68 0.91 1.11 0.82 0.79 0.73 0.71 0.96 p-value 0.190 0.454 0.750 0.373 0.169 0.508 0.554 0.660 0.699 0.315 g Diff. 1.36 0.51 0.53 0.76 0.68 0.71 0.71 0.98 1.06 1.12 p-value 0.049 0.956 0.942 0.616 0.751 0.699 0.701 0.290 0.210 0.163 All Stocks, 1972 to 1976 g 0.47 0.75 0.87 1.56 1.21 0.75 0.87 0.94 1.64 1.20 p-value 0.980 0.620 0.441 0.015 0.106 0.627 0.441 0.341 0.009 0.113 gt~ ' ! 0.80 0.40 0.50 1.24 1.21 0.65 1.26 0.63 0.70 1.39 p-value 0.539 0.998 0.966 0.093 0.106 0.794 0.084 0.821 0.718 0.041 gt~ ; ! 0.49 0.78 0.94 1.21 1.12 1.03 0.81 0.95 0.84 0.70 p-value 0.970 0.577 0.340 0.108 0.159 0.244 0.521 0.331 0.485 0.719 g Diff. 0.55 0.56 0.51 0.95 0.81 1.11 1.15 0.62 0.67 1.31 p-value 0.925 0.915 0.960 0.333 0.525 0.170 0.141 0.836 0.767 0.065 All Stocks, 1977 to 1981 g 1.16 0.73 0.76 1.16 0.82 1.14 1.01 0.87 0.86 1.79 p-value 0.138 0.665 0.617 0.136 0.506 0.147 0.263 0.428 0.449 0.003 gt~ ' ! 1.04 0.73 1.00 1.31 1.10 1.32 0.83 0.80 1.20 1.81 p-value 0.228 0.654 0.274 0.065 0.176 0.062 0.494 0.550 0.113 0.003 gt~ ; ! 0.75 0.84 0.88 0.65 0.67 0.76 1.51 1.41 0.86 0.99 p-value 0.623 0.476 0.426 0.799 0.754 0.602 0.020 0.037 0.450 0.280 g Diff. 0.67 0.94 0.88 0.70 0.65 0.70 1.11 1.29 1.16 0.70 p-value 0.767 0.335 0.423 0.708 0.785 0.716 0.172 0.073 0.137 0.713 1756 The Journal of Finance All Stocks, 1982 to 1986 g 1.57 0.99 0.59 1.46 1.47 1.04 0.87 0.68 0.76 0.90 p-value 0.015 0.276 0.883 0.029 0.027 0.232 0.431 0.742 0.617 0.387 gt~ ' ! 1.17 0.68 0.44 1.30 1.53 1.21 1.08 0.93 0.84 0.88 p-value 0.129 0.741 0.991 0.070 0.018 0.106 0.190 0.356 0.478 0.421 gt~ ; ! 0.81 1.03 0.74 0.62 0.83 1.23 0.77 0.79 0.63 0.81 p-value 0.533 0.243 0.640 0.831 0.499 0.097 0.597 0.564 0.821 0.528 g Diff. 0.51 0.79 0.70 0.81 0.74 1.21 0.73 0.75 0.93 0.74 p-value 0.961 0.567 0.717 0.532 0.643 0.107 0.657 0.623 0.352 0.642 All Stocks, 1987 to 1991 g 1.36 1.53 1.05 0.67 0.75 0.86 0.60 1.09 1.20 0.67 p-value 0.048 0.019 0.219 0.756 0.627 0.456 0.862 0.185 0.111 0.764 gt~ ' ! 0.52 1.16 1.25 0.72 1.03 0.81 0.81 0.61 1.07 0.68 p-value 0.953 0.135 0.087 0.673 0.235 0.522 0.527 0.848 0.201 0.751 gt~ ; ! 1.72 1.03 0.64 1.37 0.74 1.10 1.04 1.20 1.02 1.32 p-value 0.006 0.241 0.813 0.046 0.639 0.181 0.232 0.111 0.250 0.062 g Diff. 1.11 1.29 1.07 1.06 0.67 0.93 0.89 0.74 0.84 1.17 p-value 0.168 0.072 0.201 0.215 0.753 0.357 0.403 0.638 0.483 0.129 All Stocks, 1992 to 1996 g 1.50 1.31 1.05 1.89 1.27 0.94 1.23 0.66 1.72 1.54 p-value 0.022 0.066 0.222 0.002 0.078 0.343 0.095 0.782 0.005 0.018 gt~ ' ! 0.87 1.05 0.60 0.89 1.11 1.03 0.90 0.65 0.99 1.12 p-value 0.443 0.218 0.858 0.404 0.174 0.242 0.390 0.787 0.283 0.165 gt~ ; ! 0.72 0.66 0.75 1.42 1.02 0.58 0.61 0.64 1.36 0.93 p-value 0.670 0.778 0.624 0.036 0.246 0.895 0.854 0.813 0.048 0.357 g Diff. 0.58 0.88 0.50 0.49 0.43 0.81 0.60 0.46 0.96 0.99 p-value 0.887 0.422 0.966 0.971 0.993 0.528 0.858 0.984 0.314 0.282 Foundations of Technical Analysis 1757 Table VIII Kolmogorov–Smirnov test of the equality of conditional and unconditional one-day return distributions for Nasdaq stocks from 1962 to 1996, in five-year subperiods, and in size quintiles. Conditional returns are defined as the daily return three days following the conclusion of an occur- rence of one of 10 technical indicators: head-and-shoulders ~HS!, inverted head-and-shoulders ~IHS!, broadening top ~BTOP!, broadening bottom ~BBOT!, triangle top ~TTOP!, triangle bottom ~TBOT!, rectangle top ~RTOP!, rectangle bottom ~RBOT!, double top ~DTOP!, and double bottom ~DBOT!. All returns have been normalized by subtraction of their means and division by their standard deviations. p-values are with respect to the asymptotic distribution of the Kolmogorov–Smirnov test statistic. The symbols “t~ ' !” and “t~ ; !” indicate that the conditional distribution is also conditioned on decreasing and increasing volume trend, respectively. Statistic HS IHS BTOP BBOT TTOP TBOT RTOP RBOT DTOP DBOT All Stocks, 1962 to 1996 g 2.31 2.68 1.60 1.84 2.81 2.34 2.69 1.90 2.29 2.06 p-value 0.000 0.000 0.012 0.002 0.000 0.000 0.000 0.001 0.000 0.000 gt~ ' ! 1.86 1.53 1.35 0.99 1.97 1.95 2.16 1.73 1.38 1.94 p-value 0.002 0.019 0.052 0.281 0.001 0.001 0.000 0.005 0.045 0.001 gt~ ; ! 1.59 2.10 1.82 1.59 1.89 1.18 1.57 1.22 2.15 1.46 p-value 0.013 0.000 0.003 0.013 0.002 0.126 0.014 0.102 0.000 0.028 g Diff. 1.08 0.86 1.10 0.80 1.73 0.74 0.91 0.75 0.76 1.52 p-value 0.195 0.450 0.175 0.542 0.005 0.637 0.379 0.621 0.619 0.020 Smallest Quintile, 1962 to 1996 g 1.51 2.16 1.72 1.68 1.22 1.55 2.13 1.70 1.74 1.98 p-value 0.021 0.000 0.006 0.007 0.101 0.016 0.000 0.006 0.005 0.001 gt~ ' ! 1.16 1.30 0.85 1.14 1.25 1.62 1.43 1.05 1.08 1.95 p-value 0.139 0.070 0.463 0.150 0.089 0.010 0.033 0.216 0.191 0.001 gt~ ; ! 0.85 1.73 1.61 2.00 1.34 0.79 1.58 1.52 1.47 1.20 p-value 0.462 0.005 0.012 0.001 0.055 0.553 0.014 0.019 0.026 0.115 g Diff. 1.04 0.95 0.83 1.44 1.39 0.78 0.95 0.73 0.94 1.09 p-value 0.227 0.334 0.493 0.031 0.042 0.574 0.326 0.654 0.338 0.184 2nd Quintile, 1962 to 1996 g 1.55 1.46 0.94 1.44 1.24 1.08 1.20 1.10 1.90 1.27 p-value 0.016 0.029 0.341 0.031 0.095 0.192 0.113 0.175 0.001 0.078 gt~ ' ! 1.11 1.13 1.08 0.92 1.23 0.79 1.34 1.19 1.09 1.61 p-value 0.173 0.157 0.192 0.371 0.097 0.557 0.055 0.117 0.185 0.011 gt~ ; ! 1.37 0.87 0.73 0.97 1.38 1.29 1.12 0.91 1.12 0.94 p-value 0.048 0.439 0.665 0.309 0.044 0.073 0.162 0.381 0.165 0.343 g Diff. 1.23 0.62 0.97 0.69 1.02 1.05 1.09 0.78 0.58 0.51 p-value 0.095 0.835 0.309 0.733 0.248 0.224 0.183 0.579 0.894 0.955 1758 The Journal of Finance 3rd Quintile, 1962 to 1996 g 1.25 1.72 0.82 1.71 1.41 1.52 1.25 1.84 1.86 1.82 p-value 0.087 0.005 0.510 0.006 0.038 0.020 0.089 0.002 0.002 0.003 gt~ ' ! 0.93 1.08 0.54 1.23 1.06 1.02 0.79 1.47 1.38 0.88 p-value 0.348 0.194 0.930 0.097 0.213 0.245 0.560 0.026 0.044 0.423 gt~ ; ! 0.59 1.14 0.97 1.37 0.75 1.01 1.13 1.34 1.37 1.78 p-value 0.873 0.146 0.309 0.047 0.633 0.262 0.159 0.054 0.047 0.003 g Diff. 0.61 0.89 0.58 0.46 0.61 0.89 0.52 0.38 0.60 1.09 p-value 0.852 0.405 0.890 0.984 0.844 0.404 0.947 0.999 0.864 0.188 4th Quintile, 1962 to 1996 g 1.04 0.82 1.20 0.98 1.30 1.25 1.88 0.79 0.94 0.66 p-value 0.233 0.510 0.111 0.298 0.067 0.087 0.002 0.553 0.341 0.779 gt~ ' ! 0.81 0.54 0.57 1.05 0.92 1.06 1.23 0.72 1.53 0.87 p-value 0.528 0.935 0.897 0.217 0.367 0.215 0.097 0.672 0.019 0.431 gt~ ; ! 0.97 1.04 1.29 0.53 2.25 0.71 1.05 0.77 1.20 0.97 p-value 0.306 0.229 0.071 0.938 0.000 0.696 0.219 0.589 0.114 0.309 g Diff. 1.17 0.89 0.98 0.97 1.86 0.62 0.93 0.73 1.31 0.92 p-value 0.128 0.400 0.292 0.301 0.002 0.843 0.352 0.653 0.065 0.371 Largest Quintile, 1962 to 1996 g 1.08 1.01 1.03 0.66 0.92 0.68 0.85 1.16 1.14 0.67 p-value 0.190 0.255 0.242 0.778 0.360 0.742 0.462 0.137 0.150 0.756 gt~ ' ! 1.03 0.54 0.93 0.47 0.77 0.76 0.85 0.62 0.85 1.14 p-value 0.237 0.931 0.356 0.981 0.587 0.612 0.468 0.840 0.465 0.149 gt~ ; ! 1.18 1.39 0.50 0.93 0.88 1.25 0.77 1.13 0.98 1.12 p-value 0.123 0.041 0.967 0.358 0.415 0.089 0.597 0.156 0.292 0.160 g Diff. 0.94 1.25 0.73 0.84 0.76 1.11 0.73 0.86 0.86 0.77 p-value 0.342 0.090 0.668 0.476 0.617 0.169 0.662 0.457 0.454 0.598 All Stocks, 1962 to 1966 g 1.01 0.84 1.08 0.82 0.71 0.70 1.59 0.89 1.12 1.10 p-value 0.261 0.481 0.193 0.508 0.697 0.718 0.013 0.411 0.166 0.175 gt~ ' ! 0.95 0.65 0.41 1.05 0.51 1.13 0.79 0.93 0.93 1.21 p-value 0.322 0.798 0.997 0.224 0.956 0.155 0.556 0.350 0.350 0.108 gt~ ; ! 0.77 0.96 0.83 0.73 1.35 0.49 1.17 0.62 1.18 1.15 p-value 0.586 0.314 0.489 0.663 0.052 0.972 0.130 0.843 0.121 0.140 g Diff. 1.10 0.67 0.32 0.69 1.29 0.58 0.80 0.75 0.98 1.06 p-value 0.174 0.761 1.000 0.735 0.071 0.892 0.551 0.620 0.298 0.208 continued Foundations of Technical Analysis 1759 Table VIII—Continued Statistic HS IHS BTOP BBOT TTOP TBOT RTOP RBOT DTOP DBOT All Stocks, 1967 to 1971 g 0.75 1.10 1.00 0.74 1.27 1.35 1.16 0.74 0.74 1.21 p-value 0.636 0.175 0.273 0.637 0.079 0.052 0.136 0.642 0.638 0.107 gt~ ' ! 1.03 0.52 0.70 0.87 1.24 1.33 1.29 0.83 0.72 1.45 p-value 0.241 0.947 0.714 0.438 0.092 0.058 0.072 0.490 0.684 0.031 gt~ ; ! 1.05 1.08 1.12 0.64 0.79 0.65 0.55 0.53 0.75 0.69 p-value 0.217 0.192 0.165 0.810 0.566 0.797 0.923 0.941 0.631 0.723 g Diff. 1.24 0.89 0.66 0.78 1.07 0.88 0.88 0.40 0.91 0.76 p-value 0.093 0.413 0.770 0.585 0.203 0.418 0.423 0.997 0.385 0.602 All Stocks, 1972 to 1976 g 0.82 1.28 1.84 1.13 1.45 1.53 1.31 0.96 0.85 1.76 p-value 0.509 0.077 0.002 0.156 0.029 0.019 0.064 0.314 0.464 0.004 gt~ ' ! 0.59 0.73 Ϫ99.00 0.91 1.39 0.73 1.37 0.98 1.22 0.94 p-value 0.875 0.669 0.000 0.376 0.042 0.654 0.046 0.292 0.100 0.344 gt~ ; ! 0.65 0.73 Ϫ99.00 Ϫ99.00 Ϫ99.00 Ϫ99.00 0.59 0.76 0.78 0.65 p-value 0.800 0.653 0.000 0.000 0.000 0.000 0.878 0.611 0.573 0.798 g Diff. 0.48 0.57 Ϫ99.00 Ϫ99.00 Ϫ99.00 Ϫ99.00 0.63 0.55 0.92 0.37 p-value 0.974 0.902 0.000 0.000 0.000 0.000 0.828 0.925 0.362 0.999 All Stocks, 1977 to 1981 g 1.35 1.40 1.03 1.02 1.55 2.07 0.74 0.62 0.92 1.28 p-value 0.053 0.039 0.236 0.249 0.016 0.000 0.636 0.842 0.369 0.077 gt~ ' ! 1.19 1.47 Ϫ99.00 Ϫ99.00 0.96 0.98 0.86 0.79 0.81 0.68 p-value 0.117 0.027 0.000 0.000 0.317 0.290 0.453 0.554 0.522 0.748 gt~ ; ! 0.69 0.94 0.80 Ϫ99.00 1.46 Ϫ99.00 0.56 0.82 1.06 0.94 p-value 0.728 0.341 0.542 0.000 0.028 0.000 0.918 0.514 0.207 0.336 g Diff. 0.73 0.90 Ϫ99.00 Ϫ99.00 0.35 Ϫ99.00 0.44 0.37 0.80 0.53 p-value 0.665 0.395 0.000 0.000 1.000 0.000 0.991 0.999 0.541 0.944 1760 The Journal of Finance All Stocks, 1982 to 1986 g 1.66 1.59 1.17 0.73 1.46 1.69 1.04 1.24 2.44 1.27 p-value 0.008 0.013 0.129 0.654 0.028 0.006 0.232 0.093 0.000 0.078 gt~ ' ! 1.65 1.10 0.46 0.74 0.95 1.47 0.83 1.18 1.20 0.59 p-value 0.009 0.176 0.984 0.641 0.330 0.027 0.503 0.121 0.112 0.873 gt~ ; ! 1.13 1.31 0.86 0.42 1.17 1.04 0.97 1.13 1.68 0.89 p-value 0.153 0.065 0.445 0.995 0.129 0.231 0.302 0.155 0.007 0.405 g Diff. 0.67 0.39 0.51 0.42 0.85 0.43 0.41 0.67 0.66 0.75 p-value 0.755 0.998 0.957 0.994 0.462 0.993 0.996 0.766 0.782 0.627 All Stocks, 1987 to 1991 g 1.24 1.29 0.91 0.88 1.28 1.41 2.01 1.49 1.55 1.53 p-value 0.091 0.070 0.384 0.421 0.074 0.039 0.001 0.024 0.017 0.019 gt~ ' ! 1.05 1.00 1.00 0.78 1.68 0.92 1.67 1.25 0.61 0.86 p-value 0.221 0.266 0.274 0.580 0.007 0.369 0.008 0.087 0.849 0.448 gt~ ; ! 1.23 1.26 1.06 1.32 0.65 1.27 1.10 1.26 1.67 1.81 p-value 0.099 0.084 0.208 0.060 0.787 0.078 0.176 0.085 0.007 0.003 g Diff. 0.80 0.91 1.22 1.28 1.22 0.92 0.87 0.81 1.07 1.05 p-value 0.552 0.375 0.103 0.075 0.102 0.360 0.431 0.520 0.202 0.217 All Stocks, 1992 to 1996 g 1.21 1.61 0.84 0.90 0.97 0.91 1.60 1.51 1.13 1.00 p-value 0.108 0.011 0.476 0.394 0.299 0.379 0.012 0.021 0.156 0.265 gt~ ' ! 0.68 1.02 0.81 0.78 0.81 0.93 0.79 1.07 0.94 0.64 p-value 0.752 0.246 0.530 0.578 0.532 0.357 0.558 0.201 0.340 0.814 gt~ ; ! 1.56 0.85 0.71 1.00 1.10 1.04 1.43 0.93 0.90 1.44 p-value 0.015 0.470 0.688 0.275 0.180 0.231 0.034 0.352 0.392 0.031 g Diff. 1.45 0.59 0.94 0.62 1.15 1.14 0.64 0.52 0.59 1.35 p-value 0.030 0.879 0.346 0.840 0.139 0.148 0.814 0.953 0.874 0.052 Foundations of Technical Analysis 1761 Table IX Bootstrap percentiles for the Kolmogorov–Smirnov test of the equality of conditional and un- conditional one-day return distributions for NYSE0AMEX and Nasdaq stocks from 1962 to 1996, and for size quintiles, under the null hypothesis of equality. For each of the two sets of market data, two sample sizes, m 1 and m 2 , have been chosen to span the range of frequency counts of patterns reported in Table I. For each sample size m i , we resample one-day normal- ized returns ~with replacement! to obtain a bootstrap sample of m i observations, compute the Kolmogorov–Smirnov test statistic ~against the entire sample of one-day normalized returns!, and repeat this procedure 1,000 times. The percentiles of the asymptotic distribution are also reported for comparison. NYSE0AMEX Sample Nasdaq Sample Percentile m 1 ⌬ m 1 , n m 2 ⌬ m 2 , n ⌬ m 1 ⌬ m 1 , n m 2 ⌬ m 2 , n ⌬ All Stocks, 1962 to 1996 0.01 2076 0.433 725 0.435 0.441 1320 0.430 414 0.438 0.441 0.05 2076 0.515 725 0.535 0.520 1320 0.514 414 0.522 0.520 0.10 2076 0.568 725 0.590 0.571 1320 0.573 414 0.566 0.571 0.50 2076 0.827 725 0.836 0.828 1320 0.840 414 0.826 0.828 0.90 2076 1.219 725 1.237 1.224 1320 1.244 414 1.229 1.224 0.95 2076 1.385 725 1.395 1.358 1320 1.373 414 1.340 1.358 0.99 2076 1.608 725 1.611 1.628 1320 1.645 414 1.600 1.628 Smallest Quintile, 1962 to 1996 0.01 320 0.456 78 0.406 0.441 218 0.459 41 0.436 0.441 0.05 320 0.535 78 0.502 0.520 218 0.533 41 0.498 0.520 0.10 320 0.586 78 0.559 0.571 218 0.590 41 0.543 0.571 0.50 320 0.848 78 0.814 0.828 218 0.847 41 0.801 0.828 0.90 320 1.231 78 1.204 1.224 218 1.229 41 1.216 1.224 0.95 320 1.357 78 1.330 1.358 218 1.381 41 1.332 1.358 0.99 320 1.661 78 1.590 1.628 218 1.708 41 1.571 1.628 2nd Quintile, 1962 to 1996 0.01 420 0.445 146 0.428 0.441 305 0.458 68 0.426 0.441 0.05 420 0.530 146 0.505 0.520 305 0.557 68 0.501 0.520 0.10 420 0.580 146 0.553 0.571 305 0.610 68 0.559 0.571 0.50 420 0.831 146 0.823 0.828 305 0.862 68 0.804 0.828 0.90 420 1.197 146 1.210 1.224 305 1.265 68 1.210 1.224 0.95 420 1.349 146 1.343 1.358 305 1.407 68 1.409 1.358 0.99 420 1.634 146 1.626 1.628 305 1.686 68 1.614 1.628 3rd Quintile, 1962 to 1996 0.01 458 0.442 145 0.458 0.441 279 0.464 105 0.425 0.441 0.05 458 0.516 145 0.508 0.520 279 0.539 105 0.525 0.520 0.10 458 0.559 145 0.557 0.571 279 0.586 105 0.570 0.571 0.50 458 0.838 145 0.835 0.828 279 0.832 105 0.818 0.828 0.90 458 1.216 145 1.251 1.224 279 1.220 105 1.233 1.224 0.95 458 1.406 145 1.397 1.358 279 1.357 105 1.355 1.358 0.99 458 1.660 145 1.661 1.628 279 1.606 105 1.638 1.628 4th Quintile, 1962 to 1996 0.01 424 0.429 173 0.418 0.441 303 0.454 92 0.446 0.441 0.05 424 0.506 173 0.516 0.520 303 0.526 92 0.506 0.520 0.10 424 0.552 173 0.559 0.571 303 0.563 92 0.554 0.571 0.50 424 0.823 173 0.815 0.828 303 0.840 92 0.818 0.828 0.90 424 1.197 173 1.183 1.224 303 1.217 92 1.178 1.224 0.95 424 1.336 173 1.313 1.358 303 1.350 92 1.327 1.358 0.99 424 1.664 173 1.592 1.628 303 1.659 92 1.606 1.628 Largest Quintile, 1962 to 1996 0.01 561 0.421 167 0.425 0.441 308 0.441 108 0.429 0.441 0.05 561 0.509 167 0.500 0.520 308 0.520 108 0.508 0.520 0.10 561 0.557 167 0.554 0.571 308 0.573 108 0.558 0.571 0.50 561 0.830 167 0.817 0.828 308 0.842 108 0.816 0.828 0.90 561 1.218 167 1.202 1.224 308 1.231 108 1.226 1.224 0.95 561 1.369 167 1.308 1.358 308 1.408 108 1.357 1.358 0.99 561 1.565 167 1.615 1.628 308 1.724 108 1.630 1.628 1762 The Journal of Finance Table X Bootstrap percentiles for the Kolmogorov–Smirnov test of the equality of conditional and un- conditional one-day return distributions for NYSE0AMEX and Nasdaq stocks from 1962 to 1996, for five-year subperiods, under the null hypothesis of equality. For each of the two sets of market data, two sample sizes, m 1 and m 2 , have been chosen to span the range of frequency counts of patterns reported in Table I. For each sample size m i , we resample one-day normal- ized returns ~with replacement! to obtain a bootstrap sample of m i observations, compute the Kolmogorov–Smirnov test statistic ~against the entire sample of one-day normalized returns!, and repeat this procedure 1,000 times. The percentiles of the asymptotic distribution are also reported for comparison. NYSE0AMEX Sample Nasdaq Sample Percentile m 1 ⌬ m 1 , n m 2 ⌬ m 2 , n ⌬ m 1 ⌬ m 1 , n m 2 ⌬ m 2 , n ⌬ All Stocks, 1962 to 1966 0.01 356 0.431 85 0.427 0.441 342 0.460 72 0.417 0.441 0.05 356 0.516 85 0.509 0.520 342 0.539 72 0.501 0.520 0.10 356 0.576 85 0.559 0.571 342 0.589 72 0.565 0.571 0.50 356 0.827 85 0.813 0.828 342 0.849 72 0.802 0.828 0.90 356 1.233 85 1.221 1.224 342 1.242 72 1.192 1.224 0.95 356 1.359 85 1.363 1.358 342 1.384 72 1.339 1.358 0.99 356 1.635 85 1.711 1.628 342 1.582 72 1.684 1.628 All Stocks, 1967 to 1971 0.01 258 0.432 112 0.423 0.441 227 0.435 65 0.424 0.441 0.05 258 0.522 112 0.508 0.520 227 0.512 65 0.498 0.520 0.10 258 0.588 112 0.562 0.571 227 0.571 65 0.546 0.571 0.50 258 0.841 112 0.819 0.828 227 0.811 65 0.812 0.828 0.90 258 1.194 112 1.253 1.224 227 1.179 65 1.219 1.224 0.95 258 1.315 112 1.385 1.358 227 1.346 65 1.357 1.358 0.99 258 1.703 112 1.563 1.628 227 1.625 65 1.669 1.628 All Stocks, 1972 to 1976 0.01 223 0.439 82 0.440 0.441 58 0.433 25 0.405 0.441 0.05 223 0.518 82 0.503 0.520 58 0.495 25 0.479 0.520 0.10 223 0.588 82 0.554 0.571 58 0.542 25 0.526 0.571 0.50 223 0.854 82 0.798 0.828 58 0.793 25 0.783 0.828 0.90 223 1.249 82 1.208 1.224 58 1.168 25 1.203 1.224 0.95 223 1.406 82 1.364 1.358 58 1.272 25 1.345 1.358 0.99 223 1.685 82 1.635 1.628 58 1.618 25 1.616 1.628 All Stocks, 1977 to 1981 0.01 290 0.426 110 0.435 0.441 96 0.430 36 0.417 0.441 0.05 290 0.519 110 0.504 0.520 96 0.504 36 0.485 0.520 0.10 290 0.573 110 0.555 0.571 96 0.570 36 0.542 0.571 0.50 290 0.841 110 0.793 0.828 96 0.821 36 0.810 0.828 0.90 290 1.262 110 1.184 1.224 96 1.197 36 1.201 1.224 0.95 290 1.383 110 1.342 1.358 96 1.352 36 1.371 1.358 0.99 290 1.598 110 1.645 1.628 96 1.540 36 1.545 1.628 All Stocks, 1982 to 1986 0.01 313 0.462 106 0.437 0.441 120 0.448 44 0.417 0.441 0.05 313 0.542 106 0.506 0.520 120 0.514 44 0.499 0.520 0.10 313 0.585 106 0.559 0.571 120 0.579 44 0.555 0.571 0.50 313 0.844 106 0.819 0.828 120 0.825 44 0.802 0.828 0.90 313 1.266 106 1.220 1.224 120 1.253 44 1.197 1.224 0.95 313 1.397 106 1.369 1.358 120 1.366 44 1.337 1.358 0.99 313 1.727 106 1.615 1.628 120 1.692 44 1.631 1.628 All Stocks, 1987 to 1991 0.01 287 0.443 98 0.449 0.441 312 0.455 50 0.432 0.441 0.05 287 0.513 98 0.522 0.520 312 0.542 50 0.517 0.520 0.10 287 0.565 98 0.566 0.571 312 0.610 50 0.563 0.571 0.50 287 0.837 98 0.813 0.828 312 0.878 50 0.814 0.828 0.90 287 1.200 98 1.217 1.224 312 1.319 50 1.216 1.224 0.95 287 1.336 98 1.348 1.358 312 1.457 50 1.323 1.358 0.99 287 1.626 98 1.563 1.628 312 1.701 50 1.648 1.628 All Stocks, 1992 to 1996 0.01 389 0.438 102 0.432 0.441 361 0.447 87 0.428 0.441 0.05 389 0.522 102 0.506 0.520 361 0.518 87 0.492 0.520 0.10 389 0.567 102 0.558 0.571 361 0.559 87 0.550 0.571 0.50 389 0.824 102 0.818 0.828 361 0.817 87 0.799 0.828 0.90 389 1.220 102 1.213 1.224 361 1.226 87 1.216 1.224 0.95 389 1.321 102 1.310 1.358 361 1.353 87 1.341 1.358 0.99 389 1.580 102 1.616 1.628 361 1.617 87 1.572 1.628 Foundations of Technical Analysis 1763 ations may lead to an entirely new branch of technical analysis, one based on selecting pattern-recognition algorithms to optimize specific objective func- tions. We hope to explore these issues more fully in future research. REFERENCES Allen, Franklin, and Risto Karjalainen, 1999, Using genetic algorithms to find technical trad- ing rules, Journal of Financial Economics 51, 245–271. Beymer, David, and Tomaso Poggio, 1996, Image representation for visual learning, Science 272, 1905–1909. Blume, Lawrence, David Easley, and Maureen O’Hara, 1994, Market statistics and technical analysis: The role of volume, Journal of Finance 49, 153–181. Brock, William, Joseph Lakonishok, and Blake LeBaron, 1992, Simple technical trading rules and the stochastic properties of stock returns, Journal of Finance 47, 1731–1764. Brown, David, and Robert Jennings, 1989, On technical analysis, Review of Financial Studies 2, 527–551. Campbell, John, Andrew W. Lo, and A. Craig MacKinlay, 1997, The Econometrics of Financial Markets ~Princeton University Press, Princeton, N.J.!. Chan, Louis, Narasimhan Jegadeesh, and Joseph Lakonishok, 1996, Momentum strategies, Journal of Finance 51, 1681–1713. Chang, Kevin, and Carol Osler, 1994, Evaluating chart-based technical analysis: The head-and- shoulders pattern in foreign exchange markets, Working paper, Federal Reserve Bank of New York. Csáki, E., 1984, Empirical distribution function, in P. Krishnaiah and P. Sen, eds.: Handbook of Statistics, Vol. 4 ~Elsevier Science Publishers, Amsterdam, the Netherlands!. DeGroot, Morris, 1986, Probability and Statistics ~Addison Wesley, Reading, Mass.!. Edwards, Robert, and John Magee, 1966, Technical Analysis of Stock Trends, 5th ed. ~John Magee, Boston, Mass.!. Grundy, Bruce, and S. Martin, 1998, Understanding the nature of the risks and the source of the rewards to momentum investing, Working paper, Wharton School, University of Pennsylvania. Härdle, Wolfgang, 1990, Applied Nonparametric Regression ~Cambridge University Press, Cam- bridge, U.K.!. Hollander, Myles, and Douglas Wolfe, 1973, Nonparametric Statistical Methods ~John Wiley & Sons, New York!. Jegadeesh, Narasimhan, and Sheridan Titman, 1993, Returns to buying winners and selling losers: Implications for stock market efficiency, Journal of Finance 48, 65–91. Lo, Andrew W., and A. Craig MacKinlay, 1988, Stock market prices do not follow random walks: Evidence from a simple specification test, Review of Financial Studies 1, 41–66. Lo, Andrew W., and A. Craig MacKinlay, 1997, Maximizing predictability in the stock and bond markets, Macroeconomic Dynamics 1, 102–134. Lo, Andrew W., and A. Craig MacKinlay, 1999, A Non-Random Walk down Wall Street ~Prince- ton University Press, Princeton, N.J.!. Malkiel, Burton, 1996, A Random Walk down Wall Street: Including a Life-Cycle Guide to Per- sonal Investing ~W. W. Norton, New York!. Neely, Christopher, Peter Weller, and Robert Dittmar, 1997, Is technical analysis in the foreign exchange market profitable? A genetic programming approach, Journal of Financial and Quantitative Analysis 32, 405–426. Neely, Christopher, and Peter Weller, 1998, Technical trading rules in the European monetary system, Working paper, Federal Bank of St. Louis. Neftci, Salih, 1991, Naive trading rules in financial markets and Wiener–Kolmogorov predic- tion theory: A study of technical analysis, Journal of Business 64, 549–571. Neftci, Salih, and Andrew Policano, 1984, Can chartists outperform the market? Market effi- ciency tests for “technical analyst ,” Journal of Future Markets 4, 465–478. 1764 The Journal of Finance [...]... Anthony, and Edward Tabell, 1 964 , The case for technical analysis, Financial Analyst Journal 20, 67 – 76 Treynor, Jack, and Robert Ferguson, 1985, In defense of technical analysis, Journal of Finance 40, 757–773 Discussion NARASIMHAN JEGADEESH* Academics have long been skeptical about the usefulness of technical trading strategies The literature that evaluates the performance of such trading strategies... ~Tokyo, Japan!, 67 –75 Rouwenhorst, Geert, 1998, International momentum strategies, Journal of Finance 53, 267 –284 Simonoff, Jeffrey, 19 96, Smoothing Methods in Statistics ~Springer-Verlag, New York! Smirnov, N., 1939a, Sur les écarts de la courbe de distribution empirique, Rec Math ~Mat Sborn.) 6, 3– 26 Smirnov, N., 1939b, On the estimation of the discrepancy between empirical curves of distribution.. .Foundations of Technical Analysis 1 765 Osler, Carol, and Kevin Chang, 1995, Head and shoulders: Not just a f laky pattern, Staff Report No 4, Federal Reserve Bank of New York Poggio, Tomaso, and David Beymer, 19 96, Regularization networks for visual learning, in Shree Nayar and Tomaso Poggio, eds.: Early Visual... Vetterling, 19 86, Numerical Recipes: The Art of Scientific Computing ~Cambridge University Press, Cambridge, U.K.! Pruitt, Stephen, and Robert White, 1988, The CRISMA trading system: Who says technical analysis can’t beat the market? Journal of Portfolio Management 14, 55–58 Riesenhuber, Maximilian, and Tomaso Poggio, 1997, Common computational strategies in machine and biological vision, in Proceedings of International... usefulness of trading strategies based on various patterns They start with quantitative definitions of 10 patterns that are commonly used by chartists They then smooth the price data using kernel regressions They identify various patterns in the smoothed prices based on their definitions of these patterns Their algorithms allow them to recognize patterns objectively on the computer rather * University of Illinois... evaluating simple technical trading rules such as filter rules and moving average rules that are fairly straightforward to define and implement Lo, Mamaysky, and Wang ~hereafter LMW! move this literature forward by evaluating more complicated trading strategies used by chartists that are hard to define and implement objectively Broadly, the primary objectives of LMW are to automate the process of identifying . 1.358 0.99 458 1 .66 0 145 1 .66 1 1 .62 8 279 1 .60 6 105 1 .63 8 1 .62 8 4th Quintile, 1 962 to 19 96 0.01 424 0.429 173 0.418 0.441 303 0.454 92 0.4 46 0.441 0.05 424 0.5 06 173 0.5 16 0.520 303 0.5 26 92 0.5 06 0.520 0.10. 1.358 305 1.407 68 1.409 1.358 0.99 420 1 .63 4 1 46 1 .62 6 1 .62 8 305 1 .68 6 68 1 .61 4 1 .62 8 3rd Quintile, 1 962 to 19 96 0.01 458 0.442 145 0.458 0.441 279 0. 464 105 0.425 0.441 0.05 458 0.5 16 145 0.508. 0. 967 0.358 0.415 0.089 0.597 0.1 56 0.292 0. 160 g Diff. 0.94 1.25 0.73 0.84 0. 76 1.11 0.73 0. 86 0. 86 0.77 p-value 0.342 0.090 0 .66 8 0.4 76 0 .61 7 0. 169 0 .66 2 0.457 0.454 0.598 All Stocks, 1 962